Bibliographic record
Abstract
This thesis examines the problem of pricing and hedging spread options under market models with jumps driven by a Compound Poisson Process. Extending the work of Deng, Li and Zhou we derive the price approximation for Spread options in jump-diffusion framework. We find that the proposed model accurately approximates option prices and exhibits reasonable behavior when tested for sensitivity to the model parameters. Applying the method of Lamberton and Lepeyre, we minimize the squared error between the Spread option price and the hedge portfolio to arrive to an optimal hedging strategy for discontinuous underlying price modes. Additionally, we propose an alternative average Delta-hedging strategy that is derived by conditioning the underlying price processes on the number of jumps and summing over all the possible jump combinations; such an approach allows us to revert to a hedging problem in a Black-Scholes framework. Although the average Delta-hedging strategy offers a significantly simpler approach to hedge Spread options, we conclude that the former strategy performs better by examining the Profit and Loss Probability Density Function of the two competing strategies. Finally, we offer a model parameter calibration algorithm and test its performance using the transitional Probability Density Functions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".